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1 Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Self-fulfilling Runs: Evidence from the U.S. Life Insurance Industry Nathan C. Foley-Fisher, Borghan Narajabad, and Stephane H. Verani Please cite this paper as: Foley-Fisher, Nathan C., Borghan Narajabad and Stephane H. Verani (2015). Self-fulfilling Runs: Evidence from the U.S. Life Insurance Industry, Finance and Economics Discussion Series Washington: Board of Governors of the Federal Reserve System, NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

2 Self-fulfilling Runs: Evidence from the U.S. Life Insurance Industry Nathan Foley-Fisher Borghan Narajabad Stéphane Verani March 2015 Abstract Is liquidity creation in shadow banking vulnerable to self-fulfilling runs? Investors typically decide to withdraw simultaneously, making it challenging to identify self-fulfilling runs. In this paper, we exploit the contractual structure of funding agreement-backed securities offered by U.S. life insurers to institutional investors. The contracts allow us to obtain variation in investors expectations about other investors actions that is plausibly orthogonal to changes in fundamentals. We find that a run on U.S. life insurers during the summer of 2007 was partly due to self-fulfilling expectations. Our findings suggest that other contemporaneous runs in shadow banking by institutional investors may have had a self-fulfilling component. JEL Codes: G22, G01, G14 Keywords: Shadow banking, self-fulfilling runs, life insurance companies, funding agreement-backed securities All authors are in the Research and Statistics Division of the Federal Reserve Board of Governors. For providing valuable comments, we would like to thank, without implicating, Michael Palumbo, Mark Carey, Itay Goldstein, Stephen LeRoy, Stefan Gissler, Todd Keister, Diana Hancock, Rodney Ramcharan, Ralf Meisenzahl, Gustavo Suarez, Felton Booker, Moshe Buchinsky, Rich Rosen, Sebastian Infante Bilbao, Francesca Carapella, René Stulz, Ted Temzelides, Ricardo Correa and the seminar participants the 2014 SEM conference, 2014 Federal Reserve System Committee on Financial Structure and Regulation, Federal Reserve Board, Rice University, St Louis Fed, Philadelphia Fed, the University of Bern, NUI Maynooth, the Central Bank of Ireland, and UCSB. We are grateful to Caitlin Briglio, Della Cummings and Shannon Nitroy for exceptional research assistance. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Corresponding author: (202) , 20 th & C Street, NW, Washington, D.C

3 Introduction The financial crisis of highlighted the vulnerability of shadow banking (e.g., asset-backed commercial paper conduits) and financial markets (e.g., repo) to runs. The crisis also showed that large non-bank financial institutions, previously thought to be on the fringes of the shadow banking sector, engaged in substantial maturity and liquidity transformation, and experienced runs. 1 Yet there remains considerable debate among regulators and academics about the actual economic mechanism behind runs on shadow banks by institutional investors. While investor runs are a core issue for financial stability, theory suggests there are two distinct reasons for runs. In seminal theoretical work, Bryant (1980) and Diamond & Dybvig (1983) show that liquid liabilities are potentially vulnerable to swift changes in investors beliefs about the actions of other investors. 2 When investors withdraw based on their beliefs and their action leads other investors to withdraw, then the original belief is verified and a self-fulfilling run has occured. Such a run is in contrast to a fundamentalbased run, in which investors decide to withdraw based on, for example, changes in their liquidity demand, risk appetite, regulatory constraints, or information about the liquidity of an issuer. 3 In this alternative theory, a change in fundamentals is the key determinant of investor behavior and there is no self-fulfilling component. Identifying institutions and markets that are vulnerable to self-fulfilling runs is essential since they could originate shocks that propagate through the financial system and they have the potential to amplify and accelerate shocks elsewhere. In either case, vulnerability to self-fulfilling runs may require regulation that goes beyond better liquidity and solvency standards. However, showing that institutions and markets are plausibly vulnerable to selffulfilling runs is difficult outside of a laboratory setting. 4 The main empirical challenge 1 For instance, while the popular press attributes the fall of AIG to its AIGFP unit that unidirectionally insured vast amount of subprime MBS before the collapse in US house prices, the trigger for the largest emergency loans from the Federal Reserve came from the run by investors on the $80 billion securities lending programs from AIG s life insurers. 2 See also the work by Postlewaite & Vives (1987), Goldstein & Pauzner (2005) and Rochet (2004). 3 The information about fundamentals may be revealed to all agents, as in Allen & Gale (1998), or asymmetrically, as in Chari & Jagannathan (1988). Other studies of fundamental-based runs include Jacklin & Bhattacharya (1988), Calomiris & Gorton (1991), and Chen (1999). 4 Garratt & Keister (2009) design an experiment that shares features of the real-world environment we describe below. See also the experiments of Madies (2006), Arifovic et al. (2013) and Kiss et al. (2012). Some classic papers have shown the importance of fundamentals to bank depositors withdrawal decisions during the Great Depression (Gorton (1988), Calomiris & Gorton (1991), Saunders & Wilson (1996), and Calomiris & Mason (2003)). Recent empirical work outside the laboratory has sought to identify the determinants of bank runs: Graeve & Karas (2014) specify a structural vector autoregression with cross-sectional heterogeneity while Iyer & 2

4 to identifying self-fulfilling runs is that decisions by investors whether or not to run are made simultaneously. Investors may receive information about fundamentals, such as the liquidity of an issuer or their own liquidity demand, at the same time that they are forming beliefs about the likely actions of other investors. When we observe actions taken simultaneously, it is difficult empirically to separate runs due to changes in fundamentals from runs due to changes in expectations about other investors decisions. In this paper, we address this simultaneity problem by exploiting the contractual structure of a particular type of liquid liability issued by U.S. life insurers. Liquidity creation by U.S. life insurers emerged as a response to long-run macroeconomic and regulatory changes that affected the industry. In the traditional life insurance business model, long-term illiquid liabilities are matched with liquid assets of similar duration. The profitability of this business model relies on high returns to liquid assets and low risk-based capital requirements. So, when interest rates began falling in the late 1980s and regulatory capital requirements were increased in the early 2000s, life insurers business model was challenged. In response, life insurers adopted new models and techniques to raise their return on equity. This includes transferring insurance liabilities (risk) to off-balance sheet captive reinsurers, and funding high-yield assets with funding agreementbacked securities. For more institutional details, see Appendix A. During the early 2000s, U.S. life insurers began issuing extendible funding agreementbacked notes (XFABN). On pre-determined recurring election dates, investors in these securities decide whether or not to extend the maturity of their holding. 5 Hence, XFABN are put-able in the sense that investors have the option not to extend the maturity of any or all of their holdings. In such cases, the non-extended holdings are converted into short-term fixed maturity securities with new identifiers. Therefore, XFABN are designed to appeal to short-term investors, such as prime money market funds (MMFs), whose investment decisions may be constrained by liquidity and concentration requirements. 6 Puri (2012) use micro-level data on depositors social networks. In relation to the shadow banking system during the financial crisis, Covitz et al. (2013) document a collapse in the asset-backed commercial paper market, Gorton & Metrick (2012) identify a collapse in the repo market through a sharp rise in haircuts, while Chen et al. (2010) and Schmidt et al. (2014) study runs by investors in money market funds. 5 There is a final maturity date beyond which no extensions are possible. 6 For example, Regulation 2a-7 generally requires MMFs to hold securities with residual maturity not exceeding 397 days (SEC 2010). The initial maturity of a typical XFABN is specified such that MMFs can hold it at issuance. Thereafter, typically once every month, MMFs may elect to extend the maturity of their holding, typically by one month. This means that, from a regulatory perspective, an MMF is continuously holding a legitimate maturity bond. From the insurer s perspective, provided the MMF keeps extending the maturity, it is as if they had sold a long-term bond. 3

5 As with other types of liquid liabilities, XFABN are vulnerable to the risk that investors jointly withdraw their funds on short notice. Investors sudden withdrawal from XFABN by converting their holdings into short-dated bonds maturing around the same time could then create a liquidity shortfall for the insurer. This is especially likely since XFABN proceeds are invested in illiquid high-yield assets and other sources of liquidity could become unavailable at that time. 7 Importantly, illiquidity of an issuer may be of great concern to short-term investors who are sensitive to the timely redemption of their investments, even when the solvency of the issuer is not in doubt. 8 We document that, beginning in the third quarter of 2007, the market for XFABN collapsed as investors converted holdings worth about $15 billion (in a market with over $23 billion in outstanding securities.) We begin our analysis by modelling investors decisions to convert their holdings and exit the XFABN market. The main result is that, if the decision of other investors to convert their holdings affects the liquidity of the issuer, then there is a possibility of self-fulfilling runs. We also use the model to illustrate the salient challenges when using data on observed XFABN conversions to separate the self-fulfilling effect from the effect of fundamentals on investors decisions. Turning to our empirical analysis, the key contract characteristic we exploit is that each XFABN specifies different election dates. This allows us to separate the decisions of investors within each insurer, thereby avoiding the aforementioned simultaneity problem. In a reduced-form analysis of withdrawals, we find a statistically and economically significant relationship between the decisions of investors to withdraw and their expectations that other investors might withdraw in the future. This association is robust to controlling for cross-sectional and time fixed effects, as well as timevarying measures of stability of the insurers and of the financial sector. Of course, 7 Private observers of the insurance industry recognised early-on the liquidity risk created by combining putable liabilities with illiquid assets: Moody s believes that the put option sometimes extended to FA holders creates liquidity concerns and event risk.... The less liquid and lower quality the asset portfolio, the higher the potential for losses and increased probability of the FA issuer becoming troubled. The longer the duration of the assets, or higher potential for duration drift (a common issue for mortgage backed securities), the less likely a company can handle a put run (Moody s 1998). 8 If an insurer breaches a regulatory capital threshold, it is immediately taken over by the state. This threshold is breached much sooner than insolvency occurs. Although liability holders can be reasonably certain they will not lose their investment, there will be tremendous uncertainty over when investors will get their money back. MMFs are sensitive to any possible disruption to timely redemption of their investments, even when those investments are relatively illiquid (Hanson et al. 2013). A MMF would break the buck if on maturity the redemption of an investment were delayed by even one week. 4

6 this association could well be driven by fundamental developments, rather than by selffulfulling expectations. To build the case that there was a self-fulfilling component to the run in 2007, we adopt an instrumental variable approach based on the contractual structure of XFABN. Our strategy uses the pre-determined XFABN election dates together with variation over time in the fraction of securities that are eligible for conversion. The various XFABN issued by a given insurer typically have different election dates, but all information is known in advance to investors. Crucially, the election dates are determined when the security is issued, and are therefore plausibly exogenous to recent changes in fundamentals. This exogeneity allows us to construct an instrument for investors expectations that gets us closer to identifying the effect of changes in expectations about other investors on the payoff to an individual investor. The IV estimates suggest that investors in XFABN were sensitive to changes in their expectations that other investors would withdraw. A one standard deviation (30 percentage point) increase in an investor s expectation that other investors would withdraw is associated with an increase of 3.2 standard deviations (64 percentage points) in the probability that the investor would convert her holdings. A significant concern in this analysis is that there could be a common shock to fundamentals affecting the U.S. life industry as a whole, or a common shock to short-term investors liquidity demand. This is especially likely since the run on XFABN in 2007 coincided with runs in the asset-backed commercial paper and repo markets, and liquidity was generally evaporating around that time. In an effort to address this concern, the IV specifications allow for common fundamental shocks by including weekly time fixed effects. Separately, we also allow for insurer-specific time-varying shocks, by including monthlyinsurer fixed effects. As further controls for time-varying fundamentals, we include daily variation in the VIX, the size of the asset-backed commercial paper market, as well as insurer-specific credit default swap spreads, expected default frequencies, and stock prices. We find that our baseline IV estimate of the self-fulfilling effect is largely unaffected by these controls. To add weight to our IV findings, we implement a series of robustness tests to assess the likelihood that alternative mechanisms unrelated to self-fulfilling expectations may be driving our main results. In particular, we test whether our findings are a consequence of time-series persistence in investors decision to liquidate their holdings. We also examine 5

7 whether issuers choice of election dates at the time they issued their XFABN meant the market was designed to be fragile. We investigate whether other pre-determined variables might plausibly work as alternative instruments. And we present some evidence that our endogenous variable is correlated with recent market developments, while our instrument is not. Taken together, the results from these tests consistently suggest that there was a self-fulfilling component to the run on U.S. life insurers in Our evidence of a self-fulfilling run on U.S. life insurers contributes to a deeper understanding of the vulnerability of shadow banking to runs. While the market for XFABN is small relative to the repo and asset-backed commercial paper markets, the same institutional investors participate in all of them. Since their behaviour is likely to have been similar across markets, our study offers some evidence that there may have been a self-fulfilling component to the contemporaneous runs by institutional investors in those larger markets. 9 The remainder of the paper proceeds as follows: In Section 2 we introduce and model the XFABN issued by U.S. life insurers. Section 3 presents our data and summary statistics on these securities. Section 4 presents our main empirical results, including our IV estimates and robustness tests. We conclude in Section 5 with some remarks on broader implications and further study. 2 Model Life insurers issue FABS and invest the proceeds in a portfolio of high yield assets such as mortgages, corporate bonds and private label ABS, to earn a spread. In a typical FABS structure, shown in Figure 2, a hypothetical life insurer sells a single funding agreement to a special purpose vehicle (SPV). 10 The SPV funds the funding agreement by issuing smaller denomination FABS to institutional investors. Importantly, FABS issuance programs inherit the ratings of the sponsoring insurance company, and investors are treated pari passu with other insurance obligations since the funding agreement 9 There are two reasons why it is difficult to identify self-fulfilling runs in the repo and asset-backed commercial paper markets. First, they do not have the XFABN institutional structure. Second, unlike the run on XFABN, the run on asset-backed commercial paper and the run on repo triggered asset firesales. The absence of a firesale following the run on XFABN implies that the price of assets funded by XFABN are unlikely to have changed because of the run. The absence of this channel alleviates some of the concern that fundamentals could have biased our estimates of the effect of self-fulfilling beliefs on the decisions of institutional investors. 10 Note that FABS can only be issued by life insurers since a funding agreement is a type of annuity product. 6

8 issued to the SPV is an insurance liability. This provides FABS investors seniority over regular debt holders, and implies a lower cost of funding for the insurer relative to senior unsecured debt. 11 FABS are flexible instruments that may feature different types of embedded put option to meet demands from different types of investors, including shortterm investors, such as money market funds (MMFs). FABS designed for short-term investors are the extendible funding agreement backed notes (XFABN) that give investors the option to extend the maturity of their investment at predetermined regular intervals (usually once a month), and were subject to a run by investors in the summer of In this section, we construct a model of XFABN investors decision making to illustrate how expectations about other investors future actions may affect an investor s decision to extend or not her holding of XFABN. We show how this effect could lead to a self-fulfilling run on XFABN. We then use the model to discuss the main challenges of identifying the self-fulfilling effect from the observationally equivalent effect of fundamentals using equilibrium outcome data. We begin by formalizing the decision problem faced by XFABN investors. 12 Time is continuous, and there is a continuum of investors indexed by ι ι, each endowed with a unit of an XFABN security i I. Securities are issued by a single issuer and each unit i is expected to pay c units of coupons on specific dates t i, t i + 1, t i + 2,..., t i and a final principal payment of 1 unit at the final maturity date t i + m. Consistent with the requirements of MMFs, we assume that dividends and principal payments are not storable and must be immediately consumed to deliver utility. Investors are risk neutral, and discount the future at rate β. However, investors can only derive utility from consumption on the payment dates of their endowed security. Moreover, each investor ι might also receive an idiosyncratic shock preventing her from receiving any further utility from consumption. We will elaborate on this idiosyncratic shock below. On any of the dividend payment dates of security i, t i { t i, t i + 1,..., t i }, an investor has the option of converting a fraction or all of her holding of security i to a spinoff bullet bond, which pays the face value of the security at date t i + m. We refer to the dates on which an investor has the option to convert his investment into a short dated 11 Moreover, since a funding agreement is an insurance obligation, issuing FABS does not affect the issuing insurer s leverage, since it appears to be selling more policies. 12 The assumptions of the model are based on the actual contractual structure of XFABN. See Appendix D for an example of the first three pages of an XFABN prospectus; the overall prospectus totals over 900 pages. 7

9 bullet bond as election dates. We summarize all payments due by an issuer at time t, including predetermined payments and the payments resulting from investors converting their XFABN, by q t. The ability of the issuer to make payments at time t is summarized by N t, which we refer to as the state of fundamentals. Moreover, we assume that N t evolves according to Ṅ t = α q t r t (1) where r t is the issuer s revenue stream that follows a persistent stochastic process, q t is the total payments due on t, and α 0 is the effect of these payments on the issuer s liquidity. Specifically, the issuer could receive a liquidity shock with arrival rate F (N t ), where F ( ) is an increasing function of N t. Once the issuer receives the liquidity shock, no further payment can be made. 13 Note that when α = 0, the payments are unrelated to the issuer s liquidity. We assume that at time 0 expected and predetermined payments, denoted by q 0 t, are such that E 0 r t = α q 0 t. This implies that the expected liquidity of the issuer is constant when investors do not exercise their converting option and extend their XFABNs. 14 As mentioned before, each ι investor could receive a shock at any time t preventing her from receiving any utility after time t + m. The arrival rate of the shock is given by N ιt, which follows a random walk. Both N ιt and the idiosyncratic shocks are private information. As will be clear later, this idiosyncratic shock could be interpreted as a liquidity shock, forcing the investor to exercise her option to convert her XFABN into a short-dated bullet bond, with a maturity date that is earlier than the final maturity date of the original XFABN. 15 The timeline of the model is summarized by Figure 3. Let D ιt be the fraction of investor ι s holding of the security which is not extended (hence converted) on election date t, and therefore will mature at date t + m. It follows that at the next election date t + 1, investor ι must decide whether to extend the remaining 1 D ιt percent of her 13 Note that the issuer may not be insolvent upon receiving the liquidity shock. However, the order of payments would be disturbed. Since we assume the investors are hyper-sensitive about the timing of their consumption, the delayed payments would be useless for them. 14 Intuitively, α > 0 represents the cost of early liquidation as in the literature stemming from Diamond & Dybvig (1983). 15 We assume that the idiosyncratic shocks are uncorrelated. However, the model allows for correlated shocks, if we interpret N t to contain the correlated part of the liquidity shocks to the investors, in addition to issuer s liquidity shock. 8

10 security holding, with earliest maturity at t m. Let Q t denote the existing queue of claims on the issuer, and N ιt = (N t, r t ; N ιt ) be the summary of fundamentals affecting the issuer s ability to pay that are relevant to investor ι, as well as her own (liquidity) preferences. Conditional on not receiving an idiosyncratic (liquidity) shock and on the issuer being liquid, investor ι s decision at time t < t i is summarized by the following Bellman equation: P (Q t ; N ιt ) = max Dιt [0,1] c + D ιt e mβ [1 δ m (Q t ; N ιt )] (2) } {{ } Expected payoff at m if converting { +(1 D ιt ) e β E t [1 δ1 (Q t ; N ιt )] P ( )} Q t+1 ; N ιt+1 } {{ } Expected continuation value if extending where 1 δ m (Q t ; N ιt ) is the expected probability that neither the investor receives the idiosyncratic shock nor the issuer receives the liquidity shock in the next m periods. 16 If the option is not exercised so that D ιt = 0, the investor faces a similar decision at time t + 1 with probability 1 δ 1 (Q t ; N ιt ), and either she receives the idiosyncratic shock or the issuer becomes illiquid with probability δ 1 (Q t ; N ιt ). Note that P ( Q ti ; N ιti ) = c + e mβ (1 δ m (Q ti ; N ιti )) since there is no further election at time t i and the final maturity of security i is at time t i + m. Lemma 2.1 Given equation (1), and under mild regulatory assumptions about F ( ), the relevant part of Q t for [1 δ m (Q t ; N ιt )] is {q τ } t+m τ=t, which is the queue of payments scheduled to be made from the current period t until the maturity date of the converted bullet bond at t + m. To see this point, note that if other investors with an opportunity to exercise their option in the future choose to convert their XFABN after t, the associated final maturity payments would be scheduled for a date later than t + m, and thus would not affect the liquidity of the issuer in a significant way. 17 It follows that q t [1 δ m (Q t ; N ιt )] α t+m F t (N τ )dτ [1 δ m (Q t ; N ιt )] if t < t + m (3) 0 otherwise 16 Recall that we assume that the fair value of the investment is expected to be In fact, since converting XFABN into bullet bond means that the issuer avoids payments of c, the payments between t and t+m could potentially decrease. However, we assume c is small enough to not affect Q t significantly. 9

11 which implies that the effect of an increase in payment q t for a t (t, t + m] is negative if and only if α > 0, since F ( ) > 0. Next we study the effect of idiosyncratic and issuer liquidity shocks on investors decisions. Investor ι s decision is given by [ 0 e (m 1)β (1 δ 1 (Q t ; N ιt )) E t (1 δ1 (Q t ; N ιt )) P ( )] Q t+1 ; N ιt+1 D ιt = (4) 1 otherwise where we assume that indifferent investors always extend their XFABN. Since by converting her security the investor loses the stream of coupons, she only does so if she has serious concerns about receiving a liquidity shock or about the liquidity of the issuer. 18 That is, if N ιt increases, so that receiving the idiosyncratic shock becomes more likely, an investor would choose to convert her holding of XFABN into a short dated bullet bond, hoping that she will receive her final payment before her idiosyncratic liquidity shock arrives and she loses her appetite for consumption. Similarly, if the issuer s liquidity deteriorates and N t increases, the investor might prefer to convert her XFABN and receive her final payment before the payments are disrupted. Deterioration in the issuer s liquidity affects all investors, and could lead a significant fraction of investors to run on XFABN. The run could result from a negative shock to r t, or could be simply due to a disorderly liquidation of XFABN resulting from self-fulfilling expectations, or both. We call the negative shock to r t the fundamental effect, and we call the effect of expectations about other investors future actions on an investor s decision the self-fulfilling effect. To understand the latter effect, consider the case where investors whose election date is today believe that investors with election dates in the future will choose to withdraw. This belief induces today s decision makers to withdraw. When the resulting new additions to the payment queue induce future decision makers to withdraw on their election dates, then the belief will be self-fulfilled and a self-fulfilling run will result. Note that a small shock to r t could be amplified and accelerated by a self-fulfilling run in an interaction between the fundamental and self-fulfilling effects. The main result of this model can be summarized by Proposition 2.2 below, relegating the proof to the appendix. ( ) 18 The stream of coupons have a present value of emβ 1 e (t i t)β c. (e β 1) 10

12 Proposition 2.2 A run on XFABN could be self-fulfilling if and only if α > 0. The intuition for this result is as follows. If at time t, an investor ι expects other investors to convert their XFABN at t between t and t + 1, her expectation of the increase in the queue of payments between t + m and t + m + 1 would rise. While this change in expectation will not affect her expected value of converting her XFABN, captured by 1 δ 1 (Q t ; N ιt ), it will lower her expected value of extending the XFABN, denoted by E t P t+1, giving more incentive to convert her XFABN. 19 Moreover, the addition of her spinoff to the queue of payment would in turn have a negative effect on the expected future liquidity of the issuer, inducing other investors to convert their XFABN between t and t + 1. This realization confirms the original expectation, giving rise to a self-fulfilling run. This proposition highlights the feedback mechanism between expectations of other investors decisions and fundamentals that can arise if the decision of an investor to convert her XFABN has a negative impact on the expected value of other investors (α > 0). This mechanism would be absent if an investor s decision to convert her XFABN had no impact on the expected value of other investors (α = 0). So far we have assumed that information about the fundamentals is observable by all investors. However, asymmetric information could imply that uninformed investors act on the informed investors actions if they believe these actions contain information about the fundamentals, as in Chari & Jagannathan (1988). 20 This indirect information effect could result in a positive correlation between the uninformed investors withdrawal decisions and the previous decisions of other investors, even when α = 0, and thus the other investors decisions do not have any direct effect on the uninformed investors payoff. However, as we show in Appendix B, if α = 0 then a change in beliefs about other investors future action has no effect on the expectation about the future liquidity of the issuer, and hence affects neither informed nor uninformed investors decisions. Therefore, such beliefs cannot be self-fulfilled. 19 To see the effect of a change in the queue of payment on the expected value of extending the XFABN, recall that N t+1+m is determined by the law of motion in Equation (1). 20 In the setup of Chari & Jagannathan (1988), informed investors receive a signal about the issuer s future profitability, while uninformed investors can only observe informed investors actions. However, informed investors also experience random liquidity needs, implying that informed investors motives for withdrawals cannot be perfectly inferred by the uninformed. Thus, withdrawals may be triggered by the uninformed investors, not because withdrawals by informed investors decreases the value of the uninformed investors investment as in Diamond & Dybvig (1983), but because of the possibility of low future returns due to bad fundamentals. 11

13 Corollary 2.3 Regardless of heterogeneity in investors information about fundamentals, a run on XFABN could be a self-fulfilling run, if and only if α > Mapping decisions to observables As we will discuss in the next section, we precisely observe the aggregate fraction of XFABN that is converted at any given election date t, but do not observe individual investors conversion decisions. A question, thus, is how to use this data to learn whether there might have been a self-fulfilling component to the run on XFABN in the summer of In this sub-section, we show how observed changes in aggregate XFABN conversion across time are related to changes in investors expectations and fundamentals. Given the above framework, the aggregate fraction of XFABNs converted into shortdated bullet bonds on election date t is defined as D t (Q t ; N t ) = D ιt (Q t ; N ιt ) dµ(n ιt ) (5) where N t = (N t, r t ) summarizes the aggregate state of the issuer s liquidity, and µ( ) denotes the distribution of the investors idiosyncratic shocks, so that dµ(n ιt ) = 1. Furthermore, the expected increase at date t in other investors decisions to convert their XFABN between time t and t + 1, potentially adding to the queue of payments between t + m and t + m + 1, is defined as E t S t+1 = E t t+m+1 t+m ( ) qτ q τ t dτ where q t τ is the predetermined payments at time τ (t + m, t + m + 1] known at time t. 21 Proposition 2.4 The partial derivative is positive if and only if α > 0. D t E ts t+1 summarizes the self-fulfilling effect, and That is, at any election date t, the direct effect of a change in an investor s expectation about other investors decision to convert their XFABN in the future, on her decision to convert her XFABN at t captures the self-fulfilling effect. 21 Note that converting XFABN brings payments by the issuer to an earlier due date, reducing predetermined payments. That is, q τ t q τ 0. Conversely, when investors convert their XFABN with final maturity t at time t (t, t + 1] to a short-dated bullet bond maturing at time τ = t + m, q τ increases while q t t decreases. 12

14 While we observe D t and S t+1, the individual investor s expectation, E t S t+1, is unobservable. We invoke rational expectations to the extent that S t+1 and E t S t+1 are not orthogonal and are correlated. However, variation in S t+1 could be the result of a shock to r, thereby reflecting the liquidity of the issuer, N. And, since these shocks to fundamentals are persistent, the observed variation in D t could also be the result of a shock to fundamentals. More formally, the effect of a change in observable S t+1 on a change in D t can be expressed as dd t ds t+1 ddιt (Q = t ; N ιt ) dµ(n ιt ) ds t+1 [ t+1 ] dd ιt (Q = t ; N ιt ) dτ dµ(n ιt ) (6) t dq τ+m [ t+1 { Dιt (Q = t ; N ιt ) E tq τ+m + D ιt (Q t ; N ιt ) N } ] t N τ dτ dµ(n ιt ) t E t q τ+m q τ+m N t N τ q τ+m t+1 = t D ιt (Q t ; N ιt ) E t q τ+m } {{ } self-fulfilling effect where, as shown before, Dιt N t ) 1 + D ( ιt (Q t ; N ιt ) Nτ q ) 1 τ+m E t q τ+m N t N t N } {{ τ } dτ dµ(n ιt) fundamental effect ( qτ+m 0, and q τ+m N τ 0 from Dιτ N τ 0. Note that even if α = 0, so that Dιt(Q t ;N ιt) E tq τ = 0, a run on XFABN can occur since it could be that ddt ds t+1 > 0 from the fundamental effect. Therefore, the self-fulfilling effect cannot be identified from the effect of fundamentals without adequately controlling for the possibly confounding effect of fundamentals. The rest of the paper attempts to make some progress in identifying the self-fulfilling effect in the run on XFABN. 3 Data Before presenting the empirical results, we briefly describe our data and the magnitude of the run that occured in the XFABN market during The main source of data about XFABN is our database of all FABS issued by U.S. life insurers. 22 Our data for each 22 Our FABS database was compiled from multiple sources, covering the period beginning when FABS were first introduced in the mid-1990s to early To construct our dataset on FABS issuers, we combined information 13

15 XFABN was collected by hand from individual security prospectuses and the Bloomberg corporate action record. Each XFABN prospectus specifies the initial maturity date, the election window during which the periodic election dates occur, and when the maturity date of the XFABN may be extended. 23 If extended, the XFABN maturity date is reset to the election date plus some term pre-specified in the prospectus. Holders may continue to extend the duration of their security throughout the election window on the pre-specified election dates. When partial or whole conversions occur within the extension window, a new security identifier (CUSIP) is created and assigned to the spinoff amount. We use prospectus information and Bloomberg corporate action records to construct the universe of XFABN CUSIP identifiers, and pair them with their spinoffs CUSIP identifiers. This new security spinoff is no longer eligible for extension and has a fixed maturity date. The remaining portion of the security is eligible for extension throughout the election window and retains its original CUSIP identifier. Thus, we obtain a complete panel of all XFABN outstanding, those still eligible for extensions, and those whose holders elected to spinoff their holdings earlier than the final maturity date. In total, we record 65 XFABN issuances during the period, from which 115 individual spinoffs were issued. The average XFABN note is $450 million at issuance, while spinoffs are on average $170 million, or almost 40 percent of their parent XFABN, when created. About 65 percent of spinoffs mature in 397 days or less, consistent with an issuance strategy that targets investment by money market funds. 24 the variables used in the analysis are displayed in Table 2. Summary statistics for all Figure 4 shows the daily time series of outstanding XFABN and outstanding spinoffs from 2006 to The amount of XFABN issued almost tripled from 2004 to 2006, when issuance peaked at $6.4 billion, before falling sharply during the second half of the from various market observers and participants on FABS conduits and their issuance. We then collected data on contractual terms, outstanding amounts, and ratings for each FABS issue to obtain a complete picture of the supply of FABS at any point in time. Finally, we added data on individual conduits and insurance companies, as well as aggregate information about the insurance sector and the broader macroeconomy. A more detailed description of our FABS database, including funding agreement-backed notes and funding agreement-backed commercial paper, is provided in Appendix C. 23 Typically, holders only notify the XFABN dealer on or around each election date if they want to extend the maturity of their XFABN (either in part or the entire security). In the event that no notification is made, the security holder is assumed to have elected not to extend the security. See Appendix D for an example of the first three pages of an XFABN prospectus specifying the election dates and relevant conditions; the overall prospectus totals over 900 pages. 24 The median initial maturity at issuance for all XFABN in our sample is about 2 years, less than one-quarter of the median duration at issue of the entire sample of FABN (roughly 8 years). 14

16 financial crisis. The amount of XFABN outstanding as of June 2007 was about $23 billion, or just over 19 percent of total U.S. FABS outstanding. Issuance of XFABN since 2013 shows signs of recovery, but remains well below pre-crisis levels. 4 Empirical results The discussion in Section 2 suggests that investors decision on election date t to convert their holdings of XFABN should be positively associated with other investors decisions to convert their holdings of other XFABN before the next election date. Our empirical strategy in this section begins by establishing that there is a positive correlation between investor s decisions to convert and their expectations that holders of other XFABN will convert in future, while controlling for obvious economic fundamentals that might be driving the run. However, this correlation does not tell us whether the run is due to self-fulfilling expectations, fundamentals, or both. In the second part of our analysis, we try to draw sharper inference on the possibility that there was a self-fulfilling component using an instrumental variable (IV) approach. The unit of observation throughout our analysis is the election date t of an individual XFABN i issued by insurer j, yielding a sample of 1,467 security-election date observations from January 1, 2005 to December 31, We pay close attention to individual election dates and election windows that make each security eligible or not for conversion into a short-dated bullet bond. Our main specification is summarized by Equation 7 below. D ijt = γ 0 + γ 1 S ijt+1 + γ 2 Q jt + x jtβ + ɛ ijt (7) The dependent variable, D ijt, is the fraction of XFABN i issued by insurer j that is converted on election date t. The main explanatory variable, S ijt+1, is the fraction of all XFABN from insurer j that are converted between the current election date t and the next election date t + 1. This fraction, S ijt+1, is calculated for each election date t of each individual security i issued by j and excludes decisions made in respect of the XFABN i itself. As discussed above, S ijt+1 is an equilibrium outcome determined by selffulfilling expectations as well as fundamentals, and is therefore likely to be endogenous. In all specifications, we control for Q jt, the fraction of all XFABN from issuer j that were converted prior to election date t, a number of issuer and time specific and aggregate 15

17 controls, contained in the vector x jt. The error term ɛ ijt likely contains unobserved fundamentals, which we deal with in Section 4.2. Throughout the empirical analysis in this paper, we specify robust standard errors. 4.1 Reduced form estimates We begin our analysis by estimating the basic correlation between S ijt+1 and D ijt in a reduced form specification, controlling directly for the possibly confounding effect of observable fundamentals. The reduced form results are contained in Table 3. Column 1 of Table 3 reports the results of a regression of D ijt, the fraction of XFABN i issued by insurer j that is converted on election date t, on S ijt+1, the fraction of all XFABN from insurer j that are converted between the current election date t and the next election date t + 1, and Q jt, the fraction of all XFABN from issuer j that were converted prior to election date t. Consistent with our discussion in Section 2, we find that conversion by other XFABN holders between t and t + 1 is positively correlated with conversion on date t and is statistically significant at less than the one percent level. Column 2 of Table 3 adds insurer fixed effects to control for persistent insurer characteristics that could affect their propensity to be run on by XFABN investors. The coefficient on S ijt+1 and the R 2 are not substantially different from the specification in column 1 of Table 3, suggesting the basic correlation between S ijt+1 and D ijt is not simply driven by concerns about individual insurers. The coefficient suggests that, on average, a one standard deviation (20 percentage point) increase in investors conversion of insurer j s XFABN between election t and t + 1 is associated with a 0.8 standard deviation (25 percentage point) increase in the fraction of a particular XFABN on election date t that is converted. Column 3 of Table 3 investigates whether the correlation between D ijt and S ijt+1 could be due to a persistent autocorrelation process for S ijt+1, by decomposing Q jt into S ijt and Q jt Finding evidence of autocorrelation in S ijt+1, while controlling for Q jt 1 might cast doubt on the likelihood that coordination played a significant role in the run on XFABN. For example, if news about bad fundamentals started circulating just before election date t, one would expect D ijt to be highly correlated with the most recent 25 Recall from Section 2 that Q jt 1 = {q τ } t 1+m τ=t 1 is updated to Qjt = {qτ }t+m τ=t by adding Sijt = { } q τ q τ t t+1+m τ=t+m to the queue of payments. 16

18 decisions to convert XFABN issued by the same insurer, summarized by S ijt. The results reported in column 3 show that the coefficient on S ijt is positive but insignificant, while the coefficient on Q jt remains positive and significant at the one percent level. 26 This suggests that, consistent with the argument of Section 2, the overall size of the queue of payments and future developments that might affect the queue appear to be important for D ijt, while recent developments up to t that are summarized by S ijt are not. Column 4 of Table 3 controls for rollover risk stemming from insurers entire FABS program. Recall that insurers issue FABS that mature at different points in time. Consequently, an insurer could appear to be risky if it had a lot of FABS maturing between an election date t and the time at which the converted XFABN is set to come due, even though the amount of outstanding XFABN may be relatively small. specification of column 4 controls for the amount of fixed maturity FABS Q F ABS t Q F ABS t that mature before or on date t The coefficient on Q F ABS t The and is positive and significant, suggesting that a particular XFABN is more likely to be converted at election date t when a large fraction of fixed maturity FABNs is known to mature in the year or so after t. However, the coefficient on S ijt+1 remains materially unchanged and statistically significant at the one percent level. Column 5 of Table 3 controls for the expansion of shadow bank liquidity creation from 2005 to early It also attempts to control for the rapid development of concerns about the stability of the financial system from mid-2007 that could be a determinant of the runs on XFABN. Specifically, variables measuring the VIX and the amount of assetbacked commercial paper outstanding are added to the reduced form regression. Recall that the run on XFABN was around the same time as the run on ABCP in August 2007 (Covitz et al. 2013) and the run on repo in September 2007 (Gorton & Metrick 2012), but more than a year before the collapse of AIG. Column 6 of Table 3 adds to column 5 quarterly fixed effects to control for any common shock to the industry. 28 Column 7 26 However, we expect that S ijt+1 should be correlated with S ijt, and the coefficient on S ijt in a simple regression of D ijt on S ijt with or without Q jt is indeed significant at the one percent level. The results are available on request. 27 To be precise, Q F ABS t refers to the amount of outstanding fixed maturity FABS that are maturing before date t and Q F t ABS refers to the amount of outstanding fixed maturity FABS that will mature between t and t + 1. Note that controlling for rollover risk from fixed maturity FABS requires data on the universe of FABN, not only XFABN. See Appendix C for more details on our FABS database. 28 Note that since S ijt+1 and D ijt are zero when no run is occurring, a quarterly fixed effect is the highest frequency possible in our specification given the number of parameters to estimate and the number of insurer observations per quarter. 17

19 controls for insurer-specific time-varying fundamentals using market-based measures of issuer financial health such as insurer holding company stock prices, 5-year credit default swap spreads and 1-year Moody s KMV expected default probabilities. 29 In all three specifications, the estimated coefficient on S ijt+1 remains positive and significant, albeit somewhat smaller when including the time fixed effects. All these results suggest that the most obvious signs of deteriorating fundamentals during the onset of the global crisis cannot account for the basic correlation between S ijt+1 and D ijt. Taken together, the results in Table 3 indicate that there is a robust correlation between the probability that an investor would convert her holdings (D ijt ) and the investor s expectations about other investors likelihood of withdrawal (S ijt+1 ). This correlation survives controlling for obvious fundamentals that could affect life insurers and the broader financial system. Of course, the correlation does not imply that there was any self-fulfilling component. In particular, the likely presence of unobservable fundamentals prevents us from drawing inference on the importance of self-fulfilling expectations. We next turn to an instrumental variable approach in an effort to purge from our main explanatory variable S ijt+1 the possibly confounding effect of fundamentals, and to tease out the self-fulfilling component in the run. 4.2 Instrumental variable approach The goal of this analysis is to better estimate the effect of changes in investors expectations about S ijt+1 on D ijt. As discussed above, the effect of expectations about other investors conversions between t and t + 1 on the conversion decision is ultimately a function of the externality leading to a self-fulfilling run. 30 That is, if investors decision to convert their XFABN between two election dates t and t + 1 had no impact on the payoffs of other XFABN investors deciding to convert their XFABN at election date t, then investors expectations about other investors (conditional on the state of fundamentals at t) should have no impact on their own conversion decision. Before presenting the results, we discuss how the unusual contractual structure of XFABN can be used to construct an instrument for S ijt+1 that is plausibly unrelated to fundamentals. We then show how this instrument can be used to estimate investors 29 This specification can only be estimated on about 40 percent of the original sample, because of data availability. 30 In the language of the model discussed in Section 2, f (Q t; N ιt) / q t for t (t, t + m] 18

20 expectations about the conversion decisions of other investors between t and t + 1, and thereby estimate the effect of changes in E t S ijt+1 on D ijt. Importantly, we are not testing self-fulfilling expectations against fundamentals. Rather, our test for the self-fulfilling component is conditional on the effect of fundamentals Constructing an instrumental variable from XFABN Recall that S ijt+1 is calculated for each election date t of each individual security i issued by j and excludes decisions made in respect of the XFABN i itself. Now, consider the ratio of electable XFABN, RE ijt+1, defined as the fraction of XFABN from issuer j that is up for election between election date t and t + 1. That is, RE ijt+1 is the maximum fraction of XFABN that can be converted into short-term fixed maturity bonds between an individual XFABN i s election dates t and t + 1. For each XFABN, election details are spelled out in the XFABN prospectuses available to all investors, so that RE ijt+1 can be used by all investors to form expectations about S ijt+1. For example, if there is no XFABN from issuer j up for election between t and t + 1, everyone would know investor s expectation about S ijt+1 to be trivially 0. On the other hand, if RE ijt+1 > 0, these investors may form non-trivial expectations about the decision of other investors to convert their XFABN between t and t + 1, and their position in the queue of payments. The ratio of electable RE ijt+1 provides a link between investors ex-ante expectation E t S ijt+1 and investors ex-post decisions D ijt and S ijt+1. By definition, RE ijt+1 and S ijt+1 are bounded below by 0, and S ijt+1 is bounded above by RE ijt+1. Furthermore, note that while S ijt+1 tends to be 0 when there is no run, RE ijt+1 fluctuates over time according the set of possibly non-overlapping election cycles from all XFABN issued by insurer j. Consequently, the greater the number of XFABN outstanding with non-overlapping election cycles, the greater the fluctuations in RE ijt+1. Moreover, because RE ijt+1 is the upper bound for S ijt+1, the two variables tend to co-move positively during a run, as S ijt+1 = RE ijt+1 if all investors choose to convert their XFABN. In normal times, RE ijt+1 is pre-determined by the contractual structure of all outstanding XFABN. However, RE ijt+1 is not necessarily independent from changes in fundamentals once a run occurs. On the one hand, RE ijt+1 mechanically decreases when investors begin to convert their XFABN, since an increase in S ijt+1 necessarily implies that fewer XFABN will be up for election on future dates. Thus, if an increase in S ijt+1 is 19

21 caused by fundamentals, RE ijt+1 would be negatively correlated with fundamentals. On the other hand, RE ijt+1 could increase with an increase in XFABN issuance. For example, an insurer experiencing a run on its XFABN may try to secure new funding by issuing additional XFABNs, so that RE ijt+1 would be positively correlated with fundamentals. Thus, we construct an instrument for S ijt+1 that retains the variation of RE ijt+1 that is predetermined by the XFABN contractual structure and positively correlated with S ijt+1, but we remove any innovations to RE ijt+1 that might arise from conversion and new issues during the run period. Since the majority of XFABN in the sample are converted between August 1, 2007 and October 31, 2007, we remove any changes of RE ijt+1 from the three months leading up to each election date t (RE_ex3m ijt+1 ). Using the variation in RE_ex3m t+1 as an instrument for S ijt+1 yields estimates of the effect of the expectation of investor liquidation decisions ES ijt+1 on investors own liquidation decisions D ijt that are less likely to be biased by latent fundamental effects. Moreover, the variation of RE_ex3m ijt+1 during the run is likely orthogonal to latent fundamental effects contributing to the conversion decision. Importantly, RE_ex3m ijt+1 is not a sunspot, or coordination device for investor expectations, in the sense of Shell (1987). Rather, our empirical environment provides a variable that is correlated with investor expectations, but independent of latent fundamental effects. To see this in a simple way, consider two possible distributions of beliefs about S ijt+1 represented in Figure 6. When the overall distribution of beliefs is close to 0, as in the case g A (.), then the expectations will always be close to zero and independent of RE_ex3m ijt+1. But, as the case g B (.) shows, sometimes the expectation of S ijt+1 may be a function of RE_ex3m ijt+1. While we have no idea what (real or sunspot) variables are driving the entire distribution of beliefs to change, we can nevertheless potentially instrument for changes in the expectations about S ijt+1 using RE_ex3m ijt Instrumental variable estimates Table 4 contains our main instrumental variable (IV) results estimated using a two stage least square procedure. The first-stage regression, reported in column 1 of Table 4, regresses S ijt+1, the fraction of all XFABN from issuer j that is converted between election date t and t + 1 on RE_ex3m ijt+1, the fraction of XFABN from issuer j that is up for 20

22 election between election date t and t + 1. The regression includes the baseline controls from the specification in column 4 of Table 3. Consistent with the discussion above, the first stage results suggest there is a large positive association between S ijt+1 and RE_ex3m ijt+1 significant at less than the one percent level. The first stage results also show that the instrument passes the Stock & Yogo (2005) weak instrument test. From column 1 Table 4, a one standard deviation (10 percentage point) increase in RE_ex3m ijt+1 is associated with a 0.3 standard deviation (9 percentage point) increase in S ijt+1. Column 2 of Table 4 reports the second stage regression results, with the coefficient obtained from treating S ijt+1 with RE_ex3m ijt+1. The IV coefficient estimate is larger, but not statistically different than its OLS counterpart in the reduced form specification (column 4 of Table 3). The magnitude of the IV coefficient suggests that a one standard deviation (30 percentage point) increase in the XFABN conversion rate between t and t + 1 predicted by investors at election date t raises the probability that investors convert their XFABN at election date t by 3.2 standard deviations (64 percentage points). A significant concern in this analysis is that there could be a common shock to fundamentals affecting the U.S. life industry as a whole. This is especially likely since the run on XFABN coincided with the runs in asset-backed commercial paper and repo markets, and quickly evaporating liquidity in general. In an effort to address this concern, Columns 3 and 4 of Table 4 control further for common shocks to the industry by adding weekly time fixed effects. 31 Columns 3 and 4 of Table 4 also control for the expansion in shadow bank liquidity creation from 2005 to early 2007, and the rapid development of concerns about the stability of the financial system from mid-2007 that could be a determinant of the runs on XFABN, by including the VIX and the amount of ABCP outstanding. Intuitively, this test assumes that news about fundamentals are either broadly good or broadly bad for a whole week. On the first day of the week in which fundamentals are bad, if the fraction of electable XFABN is high, many investors will run. On the second day, if the fraction of electable XFABN is low, few investors will run. Our identification strategy could be challenged if, systematically and within each week, good news about 31 Note that unlike the reduced form specification of Table 3 for which quarterly time fixed effect were the highest frequency possible, the IV regression allows us to use a higher frequency because the value of S ijt+1 treated by RE_ex3m ijt+1 has much greater variation over the entire sample period. 21

23 fundamentals coincided with days when the fraction of electable XFABN were low and bad news coincided with days when the fraction of electable XFABN were high. However, we argue that this is an unlikely scenario since, fundamentals were worsening across capital markets during this period. As a further robustness check on fundamentals, Columns 5 and 6 of Table 4 allow for high-frequency idiosyncratic shocks by including monthly-insurer fixed effects. Columns 7 and 8 of Table 4 add daily variation in market-based measures of issuer financial health such as insurer holding company stock prices, 5-year CDS spreads and 1-year Moody s KMV Expected Default Probabilities. 32 In all these specifications, the estimated IV coefficient (S ijt+1 treated by RE_ex3m ijt+1 ) remains positive and highly significant giving us some confidence that our estimate of the coordination failure effect is not biased in obvious ways by latent fundamental effects. 4.3 Robustness to alternative mechanisms As discussed above, investors decisions to convert their XFABN could be shaped by the joint and largely unobservable variation in E t S ijt+1 and N t. Our instrumental variable approach uses the variation in RE_ex3m ijt+1 to help purge the possibly confounding effect of N t on D ijt from the equilibrium outcome S ijt+1. In this sub-section, we perform a number of tests to examine further the property of our instrument, and the robustness of our proposed mechanism to alternative explanations. The results of these tests are summarized in Table 6. A first concern is that the IV estimate of the coefficient on S ijt+1 discussed above is driven by the time-series persistence in the instrumental variable RE_ex3m ijt+1, rather than expectation about future XFABS conversion by investors. To test this hypothesis, we consider RE ijt, defined as the fraction of XFABS that is up for election between election date t 1 and the current election date t. Table 6 suggests that there is indeed a significant time-series persistence, with a correlation coefficient of 0.82 between RE_ex3m ijt+1 and RE ijt (and 0.85 between RE ijt+1 and its lag RE ijt ), respectively. Columns 1 and 2 of Table 6 report the first and second stage regression results using RE ijt as an instrument for S ijt+1, respectively. Although there is a statistically significant relationship between this alternative instrument and the endogenous variable S ijt+1 in the first stage, the results 32 This specification can only be estimated on about 40 percent of the original sample. 22

24 suggest that RE ijt is a weak instrument for S ijt+1. Moreover, the coefficient of S ijt+1 treated by RE ijt in the second stage is not statistically significant from zero. This result is consistent with the hypothesis that RE_ex3m ijt+1 can be used to form expectation about future XFABN conversion, while RE ijt cannot. A second concern is that the XFABN market could be fragile by design, which would render our instrument RE_ex3m ijt+1 correlated with fundamentals. To test this hypothesis, we define ijt+1 as the anticipated fraction of XFABS that will be up for election between election date t and t + 1, computed when the XFABN is issued. Table 6 suggests that the correlation between RE_ex3m ijt+1 and ijt+1 is only Unsurprisingly, ijt+1 is a poor instrument, as reported in column 3 and 4 of Table 6. This finding suggests that it is unlikely that insurers designed their institutional spread margin business to fail. A third concern is that there could be a mechanical relationship between the predetermined variables of the model and the liquidation decisions. To test this hypothesis, we investigate whether Q jt mechanically affects investors decisions to convert their XFABN. That is, we instrument the endogenous variable S ijt+1 with Q jt, the fraction of XFABN that has been converted up until XFABN i s election date t and that is known to come due before any amount of XFABN i converted at t comes due. Note that while Q jt is predetermined, it is not independent from fundamentals and has a direct effect on D ijt. Column 1 of Table 6 shows that the coefficient estimates on Q jt S ijt and S ijt in the reduced form specification are positive and jointly significant at less than the one percent level. However, the 2SLS results reported in column 5 and 6 of Table 6 show that the coefficient estimate on S ijt+1 instrumented with Q jt S ijt and S ijt is insignificant. More generally, this test helps shed some light on how erroneously using Q jt as an instrument for S ijt+1, a variable with a direct effect on D ijt, might bias our results. A fourth concern is that RE_ex3m ijt+1 could have a direct effect on the dependent varaible D ijt. We investigate this issue by testing whether S ijt+1 might a proxy for RE ijt+1, rather than a proxy for E t S ijt+1. Whether S ijt+1 is a proxy for RE ijt+1 would imply RE_ex3m ijt+1 could have a direct effect on D ijt, which would invalidate our instrumental variable strategy. In this case, the estimated reduced form coefficient on S ijt+1 would not capture part of the effect of E t S ijt+1 on D ijt, but instead capture the effect of RE ijt+1 on D ijt through its effect on S ijt+1. We investigate this possibility by 23

25 adding our instrument RE_ex3m ijt+1 to the baseline reduced-form specification. The results in column 7 of Table 6 suggests that the coefficient estimate on S ijt+1 is not statistically different from its counterpart in column 4 of Table 3, suggesting that S ijt+1 has a plausibly direct effect on D ijt. Lastly, while an asset fire sale could bias our estimate of the self-fulfilling effect, it is unlikely to be of great concern to institutional investors in the XFABN market. In principle, if life insurers had participated in a fire sale of assets funded by XFABN then institutional investors might have worried that the losses incurred by insurers could affect their repayment, and this fundamental effect could have contributed to the run. However, XFABN issuers had access to a backstop - the Federal Home Loan Banks. 33 As shown in Figure 5, FABS issuers accessed funding from the third quarter of 2007 by issuing funding agreements, collateralized by their real estate-linked assets, directly to one of the twelve Federal Home Loan Banks. In fact, nearly all of the increase in the Federal Home Loan Bank advances to the insurance industry from 2007 was to FABS issuers. Moreover, as shown in Figure 1 of Ashcraft et al. (2010), the cost of funding from Federal Home Loan Banks remained low and stable between June 2007 and June 2008, while the cost of funding implied by the one-month LIBOR and asset-backed commercial paper AA-rated 30 day interest rate surged, as the repo and asset-backed commercial paper markets experienced runs. Thus, the Federal Home Loan Banks played a key role in reintermediating term funding to life insurers experiencing runs by institutional investors, such as money market funds. 34 The availability of low-cost, stable Federal Home Loan Bank funding during the run and at the time the converted XFABN came due obviated the need for XFABN issuers to participate in asset fire sales. 5 Conclusion In this paper, we exploit the contractual structure of a particular type of tradable liability issued by U.S. life insurers, extendable funding agreement-backed notes (XFABN), to 33 To be a member of an Federal Home Loan Banks, a life insurer needs to have at least 10 percent of its assets linked to real estate and can obtain advances in proportion to its membership capital that are fully collateralized by real estate-linked and other eligible assets. 34 This goes beyond the point noted by Ashcraft et al. (2010) that at the outset of the financial crisis, money market investors ran away from debt [e.g. asset-backed commercial paper] issued or sponsored by depository institutions and into instruments guaranteed explicitly or implicitly by the U.S. Treasury. As a result, the Federal Home Loan Bank System was able to re-intermediate term funding to member depository institutions through advances. 24

26 identify the effect of self-fulfilling beliefs on institutional investors decisions to run on non-bank financial institutions. We find robust evidence that the run on U.S. life insurers XFABN that began in the third quarter of 2007 had a self-fulfilling component. Our results have several implications for research and macroprudential regulation. First, a large regulatory effort since the financial crisis focuses on strengthening the liquidity and solvency standards of non-bank financial institutions. However, if the self-fulfilling component identified in this paper is one of the culprits for the disruptions in non-bank financial intermediation during the crisis, more emphasis should be given to addressing the risk of self-fulfilling runs. While the market for XFABN is small relative to the repo and asset-backed commercial paper markets, the same institutional investors participate in all of them. Since their decision-making behaviour is likely to have been similar across markets, our study offers some evidence that there may have been a selffulfilling component to the runs by institutional investors in those larger shadow banking markets. Second, the Federal Home Loan Bank System provided an important backstop to U.S. life insurers during the financial crisis, possibly preventing the run on XFABN from turning into a fire sale of relatively illiquid assets around the time Fannie Mae and Freddie Mac were taken into conservatorship by the U.S. Treasury. For instance, about three quarters of the surge in Federal Home Loan Bank advances to insurance companies between 2007Q4 and 2008Q4 can be attributed to XFABN issuers at the time their spinoffs came due. However, the run on XFABN demonstrates that this backstop failed to provide effective insurance. Thus, a question is whether the ineffectiveness of the backstop was the outcome of a general lack of understanding of its existence, or evidence that it is not effective in preventing runs on liquid liabilities issued by non-banks. Lastly, U.S. financial institutions are increasing their reliance on new products such as extendible or evergreen repo in response to new rules requiring them to report longer-term financing. These repo transactions closely resemble the key features of the XFABN market studied in this paper. Understanding the vulnerability of these markets to self-fulfilling runs is important for all policymakers concerned about financial stability. 25

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